Examination of saturation coverage of polygons using random sequential adsorption algorithm

Abstract

The goal of random sequential adsorption (RSA), a time-dependent packing method, is to create a regular or asymmetric covering of an empty space that can fit in the allocated space without overlapping. The density of coverage tends to reach a limit in the infinite-time limit. We attempt to estimate saturated packing of oriented 2-D polygons, including squares(4-sides), regular pentagons (5-sides), regular hexagons (6-sides), regular heptagons (7-sides), regular octagons (8-sides), regular nonagons (9-sides), regular decagons (10-sides), and regular dodecagons (12-sides), in this study. We obtained results that are consistent with previous, extrapolation-based studies1. We utilised the "separating axis theorem" to determine if there is overlap between arriving polygons and those that have previously been placed. Saturation as a lower limit is considered to have been reached when RSA addition becomes excessively slow, according to us.